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Properties

Label 18.4.c
Level $18$
Weight $4$
Character orbit 18.c
Rep. character $\chi_{18}(7,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $6$
Newform subspaces $2$
Sturm bound $12$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 18.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(18, [\chi])\).

Total New Old
Modular forms 22 6 16
Cusp forms 14 6 8
Eisenstein series 8 0 8

Trace form

\( 6 q + 2 q^{2} + 3 q^{3} - 12 q^{4} + 18 q^{5} - 18 q^{6} + 12 q^{7} - 16 q^{8} - 105 q^{9} + O(q^{10}) \) \( 6 q + 2 q^{2} + 3 q^{3} - 12 q^{4} + 18 q^{5} - 18 q^{6} + 12 q^{7} - 16 q^{8} - 105 q^{9} + 39 q^{11} + 24 q^{12} - 24 q^{13} + 100 q^{14} + 90 q^{15} - 48 q^{16} - 78 q^{17} + 156 q^{18} + 210 q^{19} + 72 q^{20} - 36 q^{21} - 18 q^{22} - 264 q^{23} - 24 q^{24} - 219 q^{25} - 392 q^{26} - 96 q^{28} - 348 q^{29} - 288 q^{30} - 6 q^{31} + 32 q^{32} + 765 q^{33} + 90 q^{34} + 1332 q^{35} + 516 q^{36} + 192 q^{37} + 322 q^{38} - 582 q^{39} - 207 q^{41} - 816 q^{42} + 129 q^{43} - 312 q^{44} - 702 q^{45} + 504 q^{46} - 660 q^{47} - 144 q^{48} - 585 q^{49} + 614 q^{50} - 153 q^{51} - 96 q^{52} + 528 q^{53} + 954 q^{54} - 1404 q^{55} + 400 q^{56} + 987 q^{57} + 252 q^{58} - 327 q^{59} - 936 q^{60} + 858 q^{61} - 1664 q^{62} - 1794 q^{63} + 384 q^{64} + 414 q^{65} + 288 q^{66} + 1587 q^{67} + 156 q^{68} + 1494 q^{69} + 216 q^{70} - 312 q^{71} - 24 q^{72} - 258 q^{73} + 856 q^{74} + 3231 q^{75} - 420 q^{76} + 708 q^{77} + 132 q^{78} - 1482 q^{79} - 576 q^{80} + 315 q^{81} - 2916 q^{82} - 138 q^{83} + 744 q^{84} + 108 q^{85} - 86 q^{86} - 3204 q^{87} - 72 q^{88} - 3084 q^{89} - 432 q^{90} + 2508 q^{91} - 1056 q^{92} - 2634 q^{93} + 612 q^{94} - 2016 q^{95} + 384 q^{96} + 1029 q^{97} + 2604 q^{98} + 1152 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(18, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
18.4.c.a 18.c 9.c $2$ $1.062$ \(\Q(\sqrt{-3}) \) None 18.4.c.a \(-2\) \(0\) \(9\) \(31\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(3-6\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
18.4.c.b 18.c 9.c $4$ $1.062$ \(\Q(\sqrt{-3}, \sqrt{-35})\) None 18.4.c.b \(4\) \(3\) \(9\) \(-19\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-4-4\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(18, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)